MATH Seminar

Title: 3F2-hypergeometric functions and supersingular elliptic curves
Undergraduate Honors Thesis Defense: Algebra
Speaker: Sarah Pitman of Emory University
Contact: Ken Ono, ono@mathcs.emory.edu
Date: 2014-04-01 at 2:30PM
Venue: W304
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Abstract: Here we explore elliptic curves, specifically supersingular elliptic curves, and their relationship to hypergeometric functions. We begin with some background on elliptic curves, supersingularity, hypergeometric functions, and then use work of El-Guindy, Ono, Kaneko, Zagier, and Monks to extend results. In recent work, Monks described the supersingular locus of families of elliptic curves in terms of 2F1-hypergeometric functions. We “lift" his work to the level of 3F2-hypergeometric functions by means of classical transformation laws and a theorem of Clausen.